# Lifetime of battery

If I directly connect two terminals of 3V battery (negative to positive) using copper wire, would it lose all its charge faster compared to another 3V battery that is used to lighten a 1.5V bulb?

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That 1.5 V bulb is not going to survive - it'll burn out. –  MSalters Jan 26 '12 at 10:11

## 1 Answer

The battery has in both cases the same energy content, so it just depends on which method uses more energy per time. This power depends on the resistance $R$ you use to connect both terminals, with a given voltage $U$ derived from Ohm's law: $$P = U^2 /R$$ So, the smaller the resistance, the faster your battery will lose it's stored energy. The copper wire will most likely have a much smaller resistance than the 1.5V light bulb and will discharge your battery in a very short time.

For a precise estimate you also need to know the internal resistance $R_{int}$ of the battery, but that does not change the general picture: $$R = R_{int} + R_{bulb/wire}$$

Before you try it: some batteries (Li-ion, lead acid) can provide a very large current and overheat, so I would recommend not to short circuit a battery.

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So, is it best to instead use a 3V bulb for 3V battery? It is surprising to me. –  Ron Jan 26 '12 at 9:41
There's no reason why a 3V bulb would have a lower resistance than a 1.5V bulb. Those are independent variables. You might be more familiar with 40/60/100W bulbs for mains voltages. These all have different resistances despite being the same voltage. –  MSalters Jan 26 '12 at 10:13
@Ron: It is unfortunately misleading to say a "3V bulb". What that means is that it will glow and not burn out at 3V immediately. As MSalters pointed out this has nothing to do with the lifetime of the battery, the resistance or the used energy. –  Alexander Jan 26 '12 at 10:19
sorry alexander, I clicked the wrong arrow :(. If you edit I will change my vote to up –  anna v Jan 26 '12 at 15:52
@annav: no problem, thank you for the comment. –  Alexander Jan 26 '12 at 18:34